On a Class of Toeplitz + Hankel Operators

摘要

In this paper we study operators of the form M(φ)=T(φ)+H(φ)where T(φ) and H(φ) are the Toeplitz and Hankel operatorsacting on l2. We investigate the connection between Fredholmness andinvertibility of M(φ) for functions φ∈ L∞(T).Using this relationship we establish necessary and sufficientconditions for the invertibility of M(φ) with piecewisecontinuous φ. Finally, we consider several stability problemsrelated to M(φ), in particular the stability of the finitesection method.